Spin-1/2 operators exactly mapped to spinful canonical Fermi operators present in two bands

Recently it has been shown that the quantum spin-1/2 spin operators can be exactly transformed not only in spinless, but also in spinful canonical Fermi operators in 1D [\cite{JW1}], and 2D [\cite{JW2}] as well. In this paper, using the same technique based on an extended Jordan-Wigner transformation, we show in 1D, that the quantum spin-1/2 operators can be exactly transformed also in spinful canonical Fermi operators of spin-1/2 fermions that are belong to two bands.